This proposed research focuses on the development of models and statistical methods for analyzing event observations. The observations are obtained by following subjects undergoing intervention programs designed to prolong the time to the next occurrence of the recurrent event of interest (e.g., a return to substance abuse, another heart attack, another period of depression, to name a few). We will develop methods for predicting the time to the next occurrence, for comparing various types of interventions (e.g. competing treatments) and determining the relative efficacies, and for assessing which factors (covariates) significantly affect the time to the next event. Our models and methods are richer and more flexible than standard approaches, including Cox's proportional hazards model based on time-dependent covariates. In particular, our models simultaneously incorporate intervention effects, weakening (or strengthening) effects of the number of event occurrences, and the effects of the covariates. We will use the methods to analyze various data sets including hospitalization data from the US Renal Data System.